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Baire classes of Banach spaces and strongly affine functions


Author: Jirí Spurny
Journal: Trans. Amer. Math. Soc. 362 (2010), 1659-1680
MSC (2000): Primary 46A55; Secondary 26A21
DOI: https://doi.org/10.1090/S0002-9947-09-04841-7
Published electronically: October 20, 2009
MathSciNet review: 2563744
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Abstract: We construct a metrizable simplex $ X$ and a Baire-two function $ f$ on $ X$ satisfying the barycentric formula such that $ f$ is not of affine class two; i.e., there is no bounded sequence of affine Baire-one functions on $ X$ converging to $ f$. This provides an example of a Banach $ \mathcal{L}_\infty$-space $ E$ such that $ E_{2}^{**}\neq E_{\mathcal{B}_2}^{**}$.


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Additional Information

Jirí Spurny
Affiliation: Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
Email: spurny@karlin.mff.cuni.cz

DOI: https://doi.org/10.1090/S0002-9947-09-04841-7
Keywords: Simplex, strongly affine functions, barycentric formula, Baire functions, $L^1$--preduals, intrinsic Baire classes
Received by editor(s): May 24, 2007
Received by editor(s) in revised form: June 4, 2008
Published electronically: October 20, 2009
Additional Notes: This research was supported in part by the grants GA ČR 201/06/0018, GA ČR 201/07/0388, and in part by the Research Project MSM 0021620839 from the Czech Ministry of Education.
Article copyright: © Copyright 2009 American Mathematical Society

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